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Edited ch04.asciidoc with Atlas code editor

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nadams 2017-05-11 06:17:34 -07:00
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@ -147,6 +147,7 @@ The _mod p_ (modulo prime number p) indicates that this curve is over a finite f
Because this curve is defined over a finite field of prime order instead of over the real numbers, it looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical to that of an elliptic curve over real numbers. As an example, <<ecc-over-F17-math>> shows the same elliptic curve over a much smaller finite field of prime order 17, showing a pattern of dots on a grid. The +secp256k1+ bitcoin elliptic curve can be thought of as a much more complex pattern of dots on a unfathomably large grid. Because this curve is defined over a finite field of prime order instead of over the real numbers, it looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical to that of an elliptic curve over real numbers. As an example, <<ecc-over-F17-math>> shows the same elliptic curve over a much smaller finite field of prime order 17, showing a pattern of dots on a grid. The +secp256k1+ bitcoin elliptic curve can be thought of as a much more complex pattern of dots on a unfathomably large grid.
[[ecc-over-F17-math]] [[ecc-over-F17-math]]
[role="smallersixty"]
.Elliptic curve cryptography: visualizing an elliptic curve over F(p), with p=17 .Elliptic curve cryptography: visualizing an elliptic curve over F(p), with p=17
image::images/mbc2_0403.png["ecc-over-F17-math"] image::images/mbc2_0403.png["ecc-over-F17-math"]